%I #9 Jun 19 2022 02:19:39
%S 72,212,212,576,560,576,1696,1400,1400,1696,4656,3796,3240,3796,4656,
%T 13736,9780,8224,8224,9780,13736,38064,27080,19952,19584,19952,27080,
%U 38064,112504,71244,52328,45128,45128,52328,71244,112504,314448,200164
%N T(n,k) is the number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).
%H R. H. Hardin, <a href="/A235186/b235186.txt">Table of n, a(n) for n = 1..284</a>
%F Empirical for column k (the k=4..7 recurrence works also for k=1..3; apparently all rows and columns satisfy the same order 27 recurrence):
%F k=1: a(n) = 16*a(n-2) -65*a(n-4) +14*a(n-6).
%F k=2: [order 18].
%F k=3: [order 26].
%F k=4..7: [same order 27 recurrence].
%e Table starts
%e 72 212 576 1696 4656 13736 38064 112504 314448
%e 212 560 1400 3796 9780 27080 71244 200164 535384
%e 576 1400 3240 8224 19952 52328 131120 352000 903544
%e 1696 3796 8224 19584 45128 112432 270056 694680 1719360
%e 4656 9780 19952 45128 99096 236376 545768 1351904 3234336
%e 13736 27080 52328 112432 236376 540368 1204056 2877232 6679048
%e 38064 71244 131120 270056 545768 1204056 2598040 6019088 13595968
%e 112504 200164 352000 694680 1351904 2877232 6019088 13521264 29758464
%e 314448 535384 903544 1719360 3234336 6679048 13595968 29758464 64019304
%e 930968 1520236 2468016 4527576 8236464 16488928 32649376 69567168 146227600
%e Some solutions for n=4, k=4:
%e 4 1 3 1 3 1 3 1 4 2 5 3 5 3 4 0 3 1 5 2
%e 1 3 0 3 0 4 1 4 2 5 1 4 1 4 0 3 1 4 3 5
%e 5 2 4 2 4 2 4 2 5 3 3 1 3 1 2 0 3 1 5 2
%e 2 4 1 4 1 4 1 4 2 5 1 4 1 4 0 3 1 4 3 5
%e 5 2 4 2 4 2 4 2 5 3 2 0 2 0 1 0 3 1 5 2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 04 2014